/* SPDX-License-Identifier: SunMicrosystems */
/* Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. */

/**
 *
 * This family of functions implements the value of :math:`x` raised to the
 * power of :math:`y`.
 *
 * Synopsis
 * ========
 *
 * .. code-block:: c
 *
 *     #include <math.h>
 *     float powf(float x, float y);
 *     double pow(double x, double y);
 *     long double powl(long double x, long double y);
 *
 * Description
 * ===========
 *
 * ``pow`` computes the value of :math:`x` raised to the power of :math:`y`.
 *
 * Mathematical Function
 * =====================
 *
 * .. math::
 *
 *    pow(x, y) \approx x^y
 *
 * Returns
 * =======
 *
 * ``pow`` returns the value of :math:`x` raised to the power of :math:`y`.
 *
 * Exceptions
 * ==========
 *
 * Raise ``invalid operation`` exception when :math:`x` is finite and negative
 * and :math:`y` is finite and not an integer value.
 *
 * Raise ``divide by zero`` exception when :math:`x` is zero and :math:`y` is a
 * negative odd integer value.
 *
 * Raise ``overflow`` exception when the magnitude of the result is too large.
 *
 * .. May raise ``underflow`` exception.
 *
 * Output map
 * ==========
 *
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+
 * | pow(x,y)                                   | x                                                                                                                                                                                                                                                                                                                                 |
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+
 * | y                                          | :math:`-Inf`             | :math:`< -1`             | :math:`-1`               | :math:`]-1,-0[`          | :math:`-0`               | :math:`+0`               | :math:`]+0,+1[`          | :math:`+1`               | :math:`> +1`             | :math:`+Inf`             | :math:`qNaN`             | :math:`sNaN`             |
 * +============================================+==========================+==========================+==========================+==========================+==========================+==========================+==========================+==========================+==========================+==========================+==========================+==========================+
 * | :math:`-Inf`                               | :math:`+0`                                          | :math:`+1`               | :math:`+Inf`                                                                                              | :math:`+1`               | :math:`+0`                                          | :math:`qNaN`             | :math:`qNaN`             |
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+                          +--------------------------+--------------------------+                          +                          +
 * | :math:`\{2k + 1 : k \in \mathbb{Z}_{<0}\}` | :math:`-0`               | :math:`x^y`                                                                    | :math:`-Inf`             | :math:`+Inf`             | :math:`x^y`              |                          | :math:`x^y`              | :math:`+0`               |                          |                          |
 * +--------------------------------------------+--------------------------+                                                                                +--------------------------+--------------------------+                          +                          +                          +                          +                          +                          +
 * | :math:`\{2k : k \in \mathbb{Z}_{<0}\}`     | :math:`+0`               |                                                                                | :math:`+Inf`                                        |                          |                          |                          |                          |                          |                          |
 * +--------------------------------------------+                          +--------------------------+--------------------------+--------------------------+                                                     +                          +                          +                          +                          +                          +                          +
 * | :math:`< 0\ \wedge \notin \mathbb{Z}`      |                          | :math:`qNaN`                                                                   |                                                     |                          |                          |                          |                          |                          |                          |
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+                          +
 * | :math:`-0`                                 | :math:`+1`                                                                                                                                                                                                                                                                                             |                          |
 * +--------------------------------------------+                                                                                                                                                                                                                                                                                                        +                          +
 * | :math:`+0`                                 |                                                                                                                                                                                                                                                                                                        |                          |
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+                          +
 * | :math:`> 0\ \wedge \notin \mathbb{Z}`      | :math:`+Inf`             | :math:`qNaN`                                                                   | :math:`+0`                                          | :math:`x^y`              | :math:`+1`               | :math:`x^y`              | :math:`+Inf`             | :math:`qNaN`             |                          |
 * +--------------------------------------------+                          +--------------------------+--------------------------+--------------------------+                                                     +                          +                          +                          +                          +                          +                          +
 * | :math:`\{2k : k \in \mathbb{Z}_{>0}\}`     |                          | :math:`x^y`                                                                    |                                                     |                          |                          |                          |                          |                          |                          |
 * +--------------------------------------------+--------------------------+                                                                                +--------------------------+--------------------------+                          +                          +                          +                          +                          +                          +
 * | :math:`\{2k - 1 : k \in \mathbb{Z}_{>0}\}` | :math:`-Inf`             |                                                                                | :math:`-0`               | :math:`+0`               |                          |                          |                          |                          |                          |                          |
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+                          +--------------------------+--------------------------+                          +                          +
 * | :math:`+Inf`                               | :math:`+Inf`                                        | :math:`+1`               | :math:`+0`                                                                                                |                          | :math:`+Inf`                                        |                          |                          |
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+                          +--------------------------+--------------------------+--------------------------+                          +
 * | :math:`qNaN`                               | :math:`qNaN`                                                                                                                                                                               |                          | :math:`qNaN`                                                                   |                          |
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+
 * | :math:`sNaN`                               | :math:`qNaN`                                                                                                                                                                                                                                                                                                                      |
 * +--------------------------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+--------------------------+
 *
 *///

#include <math.h>
#include "../common/tools.h"

#ifndef __LIBMCS_DOUBLE_IS_32BITS

static const double
bp[]     = {1.0, 1.5},
dp_h[]   = { 0.0, 5.84962487220764160156e-01}, /* 0x3FE2B803, 0x40000000 */
dp_l[]   = { 0.0, 1.35003920212974897128e-08}, /* 0x3E4CFDEB, 0x43CFD006 */
zero     =  0.0,
one      =  1.0,
two      =  2.0,
two53    =  9007199254740992.0,          /* 0x43400000, 0x00000000 */
/* poly coefs for (3/2)*(log(x)-2s-2/3*s**3 */
L1       =  5.99999999999994648725e-01,  /* 0x3FE33333, 0x33333303 */
L2       =  4.28571428578550184252e-01,  /* 0x3FDB6DB6, 0xDB6FABFF */
L3       =  3.33333329818377432918e-01,  /* 0x3FD55555, 0x518F264D */
L4       =  2.72728123808534006489e-01,  /* 0x3FD17460, 0xA91D4101 */
L5       =  2.30660745775561754067e-01,  /* 0x3FCD864A, 0x93C9DB65 */
L6       =  2.06975017800338417784e-01,  /* 0x3FCA7E28, 0x4A454EEF */
P1       =  1.66666666666666019037e-01,  /* 0x3FC55555, 0x5555553E */
P2       = -2.77777777770155933842e-03,  /* 0xBF66C16C, 0x16BEBD93 */
P3       =  6.61375632143793436117e-05,  /* 0x3F11566A, 0xAF25DE2C */
P4       = -1.65339022054652515390e-06,  /* 0xBEBBBD41, 0xC5D26BF1 */
P5       =  4.13813679705723846039e-08,  /* 0x3E663769, 0x72BEA4D0 */
lg2      =  6.93147180559945286227e-01,  /* 0x3FE62E42, 0xFEFA39EF */
lg2_h    =  6.93147182464599609375e-01,  /* 0x3FE62E43, 0x00000000 */
lg2_l    = -1.90465429995776804525e-09,  /* 0xBE205C61, 0x0CA86C39 */
ovt      =  8.0085662595372944372e-0017, /* -(1024-log2(ovfl+.5ulp)) */
cp       =  9.61796693925975554329e-01,  /* 0x3FEEC709, 0xDC3A03FD =2/(3ln2) */
cp_h     =  9.61796700954437255859e-01,  /* 0x3FEEC709, 0xE0000000 =(float)cp */
cp_l     = -7.02846165095275826516e-09,  /* 0xBE3E2FE0, 0x145B01F5 =tail of cp_h*/
ivln2    =  1.44269504088896338700e+00,  /* 0x3FF71547, 0x652B82FE =1/ln2 */
ivln2_h  =  1.44269502162933349609e+00,  /* 0x3FF71547, 0x60000000 =24b 1/ln2*/
ivln2_l  =  1.92596299112661746887e-08;  /* 0x3E54AE0B, 0xF85DDF44 =1/ln2 tail*/

double pow(double x, double y)
{
    double z, ax, z_h, z_l, p_h, p_l;
    double _y1, t1, t2, r, s, sign, t, u, v, w;
    int32_t i, j, k, yisint, n;
    int32_t hx, hy, ix, iy;
    uint32_t lx, ly;

    EXTRACT_WORDS(hx, lx, x);
    EXTRACT_WORDS(hy, ly, y);
    ix = hx & 0x7fffffff;
    iy = hy & 0x7fffffff;

    /* y==zero: x**0 = 1 unless x is snan */
#ifdef __LIBMCS_FPU_DAZ
    if (iy < 0x00100000) {
#else
    if ((iy | ly) == 0) {
#endif /* defined(__LIBMCS_FPU_DAZ) */
        if (__issignaling(x) != 0) {
            return x + y;
        }

        return one;
    }

    /* x|y==NaN return NaN unless x==1 then return 1 */ /* For performance: don't use isnan */
    if (ix > 0x7ff00000 || ((ix == 0x7ff00000) && (lx != 0)) ||
        iy > 0x7ff00000 || ((iy == 0x7ff00000) && (ly != 0))) {
        if (((hx - 0x3ff00000) | lx) == 0 && __issignaling(y) == 0) {
            return one;
        } else {
            return x + y;
        }
    }

#ifdef __LIBMCS_FPU_DAZ
    x *= __volatile_one;
    y *= __volatile_one;

    EXTRACT_WORDS(hx, lx, x);
    EXTRACT_WORDS(hy, ly, y);
    ix = hx & 0x7fffffff;
    iy = hy & 0x7fffffff;
#endif /* defined(__LIBMCS_FPU_DAZ) */

    /* determine if y is an odd int when x < 0
     * yisint = 0    ... y is not an integer
     * yisint = 1    ... y is an odd int
     * yisint = 2    ... y is an even int
     */
    yisint  = 0;

    if (hx < 0) {
        if (iy >= 0x43400000) {
            yisint = 2;               /* even integer y */
        } else if (iy >= 0x3ff00000) {
            k = (iy >> 20) - 0x3ff;   /* exponent */

            if (k > 20) {
                j = ly >> (52 - k);

                if (((uint32_t)j << (52 - k)) == ly) {
                    yisint = 2 - (j & 1);
                }
            } else if (ly == 0) {
                j = iy >> (20 - k);

                if ((j << (20 - k)) == iy) {
                    yisint = 2 - (j & 1);
                }
            } else {
                /* No action required */
            }
        } else {
            /* No action required */
        }
    }

    /* special value of y */
    if (ly == 0) {
        if (iy == 0x7ff00000) {            /* y is +-inf */
            if (((ix - 0x3ff00000) | lx) == 0) {
                return one;                /* +-1**+-inf = 1 */
            } else if (ix >= 0x3ff00000) { /* (|x|>1)**+-inf = inf,0 */
                return (hy >= 0) ? y : zero;
            } else {                       /* (|x|<1)**-,+inf = inf,0 */
                return (hy < 0) ? -y : zero;
            }
        }

        if (iy == 0x3ff00000) {            /* y is  +-1 */
            if (hy < 0) {
                return one / x;
            } else {
                return x;
            }
        }

        if (hy == 0x40000000) {
            return x * x;                  /* y is  2 */
        }

        if (hy == 0x3fe00000) {            /* y is  0.5 */
            if (hx >= 0) {                 /* x >= +0 */
                return sqrt(x);
            }
        }
    }

    ax   = fabs(x);

    /* special value of x */
    if (lx == 0) {
        if (ix == 0x7ff00000 || ix == 0 || ix == 0x3ff00000) {
            z = ax;                        /*x is +-0,+-inf,+-1*/

            if (hy < 0) {                  /* z = (1/|x|) */
                if (ix == 0x7ff00000) {
                    z = zero;
                } else if (ix == 0) {
                    z = __raise_div_by_zero(z);
                } else {
                    /* No action required */
                }
            }

            if (hx < 0) {
                if (((ix - 0x3ff00000) | yisint) == 0) {
                    z = __raise_invalid(); /* (-1)**non-int is NaN */
                } else if (yisint == 1) {
                    z = -z;                /* (x<0)**odd = -(|x|**odd) */
                } else {
                    /* No action required */
                }
            }

            return z;
        }
    }

    n = ((uint32_t)hx >> 31U) - 1U;

    /* (x<0)**(non-int) is NaN */
    if ((n | yisint) == 0) {
        return __raise_invalid();
    }

    sign = one; /* (sign of result -ve**odd) = -1 else = 1 */
    if ((n | (yisint - 1)) == 0) {
        sign = -one;    /* (-ve)**(odd int) */
    }

    /* |y| is huge */
    if (iy > 0x42000000) {     /* if |y| > ~2**33 (does not regard mantissa) */
        if (iy > 0x43f00000) { /* if |y| > ~2**64, must o/uflow and y is an even integer */
            if (ix <= 0x3fefffff) { /* |x| < 1 */
                return (hy < 0) ? __raise_overflow(one) : __raise_underflow(one);
            } else {                /* |x| > 1 */
                return (hy > 0) ? __raise_overflow(one) : __raise_underflow(one);
            }
        }

        /* over/underflow if x is not close to one */
        if (ix < 0x3fefffff) {
            return (hy < 0) ? __raise_overflow(sign) : __raise_underflow(sign);
        }

        if (ix > 0x3ff00000) {
            return (hy > 0) ? __raise_overflow(sign) : __raise_underflow(sign);
        }

        /* now |1-x| is tiny <= 2**-20, suffice to compute
           log(x) by x-x^2/2+x^3/3-x^4/4 */
        t = ax - 1;      /* t has 20 trailing zeros */
        w = (t * t) * (0.5 - t * (0.3333333333333333333333 - t * 0.25));
        u = ivln2_h * t;  /* ivln2_h has 21 sig. bits */
        v = t * ivln2_l - w * ivln2;
        t1 = u + v;
        SET_LOW_WORD(t1, 0);
        t2 = v - (t1 - u);
    } else {
        double s2, s_h, s_l, t_h, t_l;
        n = 0;

        /* take care subnormal number */
        if (ix < 0x00100000) {
            ax *= two53;
            n -= 53;
            GET_HIGH_WORD(ix, ax);
        }

        n  += ((ix) >> 20) - 0x3ff;
        j  = ix & 0x000fffff;
        /* determine interval */
        ix = j | 0x3ff00000;      /* normalize ix */

        if (j <= 0x3988E) {
            k = 0;                /* |x|<sqrt(3/2) */
        } else if (j < 0xBB67A) {
            k = 1;                /* |x|<sqrt(3)   */
        } else {
            k = 0;
            n += 1;
            ix -= 0x00100000;
        }

        SET_HIGH_WORD(ax, ix);

        /* compute s = s_h+s_l = (x-1)/(x+1) or (x-1.5)/(x+1.5) */
        u = ax - bp[k];      /* bp[0]=1.0, bp[1]=1.5 */
        v = one / (ax + bp[k]);
        s = u * v;
        s_h = s;
        SET_LOW_WORD(s_h, 0);
        /* t_h=ax+bp[k] High */
        t_h = zero;
        SET_HIGH_WORD(t_h, ((ix >> 1) | 0x20000000) + 0x00080000 + (k << 18));
        t_l = ax - (t_h - bp[k]);
        s_l = v * ((u - s_h * t_h) - s_h * t_l);
        /* compute log(ax) */
        s2 = s * s;
        r = s2 * s2 * (L1 + s2 * (L2 + s2 * (L3 + s2 * (L4 + s2 * (L5 + s2 * L6)))));
        r += s_l * (s_h + s);
        s2  = s_h * s_h;
        t_h = 3.0 + s2 + r;
        SET_LOW_WORD(t_h, 0);
        t_l = r - ((t_h - 3.0) - s2);
        /* u+v = s*(1+...) */
        u = s_h * t_h;
        v = s_l * t_h + t_l * s;
        /* 2/(3log2)*(s+...) */
        p_h = u + v;
        SET_LOW_WORD(p_h, 0);
        p_l = v - (p_h - u);
        z_h = cp_h * p_h;      /* cp_h+cp_l = 2/(3*log2) */
        z_l = cp_l * p_h + p_l * cp + dp_l[k];
        /* log2(ax) = (s+..)*2/(3*log2) = n + dp_h + z_h + z_l */
        t = (double)n;
        t1 = (((z_h + z_l) + dp_h[k]) + t);
        SET_LOW_WORD(t1, 0);
        t2 = z_l - (((t1 - t) - dp_h[k]) - z_h);
    }

    /* split up y into _y1+y2 and compute (_y1+y2)*(t1+t2) */
    _y1  = y;
    SET_LOW_WORD(_y1, 0);
    p_l = (y - _y1) * t1 + y * t2;
    p_h = _y1 * t1;
    z = p_l + p_h;
    EXTRACT_WORDS(j, i, z);

    if (j >= 0x40900000) {                       /* z >= 1024 */
        if (((j - 0x40900000) | i) != 0) {       /* if z > 1024 */
            return __raise_overflow(sign);
        } else {
            if (p_l + ovt > z - p_h) {
                return __raise_overflow(sign);
            }
        }
    } else if ((j & 0x7fffffff) >= 0x4090cc00) { /* z <= -1075 */
        if (((j - 0xc090cc00U) | i) != 0) {      /* z < -1075 */
            return __raise_underflow(sign);
        } else {
            if (p_l <= z - p_h) {
                return __raise_underflow(sign);
            }
        }
    } else {
        /* No action required */
    }

    /*
     * compute 2**(p_h+p_l)
     */
    i = j & 0x7fffffff;
    k = (i >> 20) - 0x3ff;
    n = 0;

    if (i > 0x3fe00000) {                        /* if |z| > 0.5, set n = [z+0.5] */
        n = j + (0x00100000 >> (k + 1));
        k = ((n & 0x7fffffff) >> 20) - 0x3ff;    /* new k for n */
        t = zero;
        SET_HIGH_WORD(t, n & ~(0x000fffff >> k));
        n = ((n & 0x000fffff) | 0x00100000) >> (20 - k);

        if (j < 0) {
            n = -n;
        }

        p_h -= t;
    }

    t = p_l + p_h;
    SET_LOW_WORD(t, 0);
    u = t * lg2_h;
    v = (p_l - (t - p_h)) * lg2 + t * lg2_l;
    z = u + v;
    w = v - (z - u);
    t  = z * z;
    t1  = z - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5))));
    r  = (z * t1) / (t1 - two) - (w + z * w);
    z  = one - (r - z);
    GET_HIGH_WORD(j, z);
    j += (n << 20);

    if ((j >> 20) <= 0) {
        z = scalbn(z, (int32_t)n);                    /* subnormal output */
    } else {
        SET_HIGH_WORD(z, j);
    }

    return sign * z;
}

#ifdef __LIBMCS_LONG_DOUBLE_IS_64BITS

long double powl(long double x, long double y)
{
    return (long double) pow((double) x, (double) y);
}

#endif /* #ifdef __LIBMCS_LONG_DOUBLE_IS_64BITS */
#endif /* #ifndef __LIBMCS_DOUBLE_IS_32BITS */
